You definitely shouldn’t put energy into a friendship if you feel like the other person isn’t interested, but be careful with this mindset. I’ve seen plenty of cases where this becomes such a fear and habit, that the person never reaches out to anyone, because they’re waiting to be talked to first as a test. It becomes a self fulfilling prophecy.

Others are also busy. Others might also be waiting for you to reach out. If you want a friendship to happen it’s OK to initiate. People will often appreciate it.